Optimization & Operations Research
Javad Gerami; Alireza Davoodi
Abstract
Two-stage network Data Envelopment Analysis (DEA) models under variable returns to scale (VRS) suffer from a well-known pitfall: efficiency score decomposition and frontier projection can be mutually inconsistent, undermining both the theoretical foundations and practical interpretability of the results. ...
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Two-stage network Data Envelopment Analysis (DEA) models under variable returns to scale (VRS) suffer from a well-known pitfall: efficiency score decomposition and frontier projection can be mutually inconsistent, undermining both the theoretical foundations and practical interpretability of the results. A further limitation is the universal assumption of strong disposability for all inputs and outputs, which is unrealistic when variables are structurally or statistically interdependent—as is common in healthcare settings. This paper addresses both issues simultaneously by developing a novel two-stage network DEA model under hybrid disposability (HD) technology, which allows selective strong or weak disposability for subsets of closely related inputs, intermediate measures, and outputs. We formally derive the efficiency decomposition and frontier projection under HD technology, establish theoretical consistency between the envelopment and multiplier forms, and prove that the proposed model yields Pareto-efficient targets. The model captures synergistic scale effects across stages and preserves structural dependencies between them, thereby providing a more realistic representation of multi-stage production systems. The practical relevance and advantages of the proposed framework are demonstrated through an empirical case study involving 32 Iranian healthcare centers operating under a two-stage network structure with interdependent variables.
